Research done in the mid 1980s indicated that 80% of grizzly bears in the greater yellowstone ecosystem entered their den for hibernation by the last day of november. this has come into question as of late. researchers have hypothesized that climate change has postponed bears entering hibernation until later in the scason; that is, researchers believe that a smaller percentage of bears are entering their den for hibernation by the last day of november. sixty-two yellowstone grizzly bears are being tracked via radio mon itors, which allow scientists to pinpoint when the bears enter their dens with a high degree of accuracy. of the sixty-two yellowstone grizzly bears being tracked, forty-two had entered their den for hibernation by the last day of november. d. [3 pts) where is the distribution of simulated "number of successes" centered? explain, in context, why this makes sense. problem 6 continued. 14 pts) how could we use coins, a spinner, or cards to simulate one of the samples in the e. above simulation? circle all that apply (a) flip a coin 62 times, where heads represents "hibernate by november 30." count the number of heads in 62 flips. (8) create a spinner with 80% shaded to represent "hibernate by november 30." spin the spinner 62 times and count the number of times the spinner lands in the shaded area. (c) have 8 black cards and 2 red cards where black represents "hibernate by november 30" draw with replacement from the cards 62 times and count the number of times a black card is drawn. (d) create a spinner with 68 % shaded to represent "hibernate by november 30." spin the spinner 62 times and count the number of times the spinner lands in the shaded area. f. [4 pts] the simulation-based p-value for this test is 0.0153. interpret this value in the context of the problem. (note: this should not be a strength of evidence statement, but rather an interpretation of what the value 0.0153 represents in context of the problem.) g [4 pts) recall that in this sample, 42 of 62 bears had entered their den for hibernation by the last day of november. for each of the following sample results, circle whether the p- value would increase, decrease, or remain the same if we were to track another sample of yellowstone grizzly bears. (i) 126 of 186 bears had entered their den for hibernation by the last day of november increase decrease remain the same (ii) 45 of 62 bears had entered their den for hibernation by the last day of november increase remain the same decrease